Representation of the non-dominated set in biobjective discrete optimization
This paper introduces several algorithms for finding a representative subset of the non-dominated point set of a biobjective discrete optimization problem with respect to uniformity, coverage and the ϵ-indicator. We consider the representation problem itself as multiobjective, trying to find a good...
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| Veröffentlicht in: | Computers & operations research 2015-11, Vol.63, p.172-186 |
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| creator | Vaz, Daniel Paquete, Luís Fonseca, Carlos M. Klamroth, Kathrin Stiglmayr, Michael |
| description | This paper introduces several algorithms for finding a representative subset of the non-dominated point set of a biobjective discrete optimization problem with respect to uniformity, coverage and the ϵ-indicator. We consider the representation problem itself as multiobjective, trying to find a good compromise between these quality measures. These representation problems are formulated as particular facility location problems with a special location structure, which allows for polynomial-time algorithms in the biobjective case based on the principles of dynamic programming and threshold approaches. In addition, we show that several multiobjective variants of these representation problems are also solvable in polynomial time. Computational results obtained by these approaches on a wide range of randomly generated point sets are presented and discussed.
•We formulate the representation problem in two dimensions for three different measures: uniformity, coverage, and є-indicator.•We present algorithms that solve the representation problems for the three measures in polynomial time.•We consider multiobjective variants of representation problems, and present polynomial time algorithms to solve them.•We present and discuss experimental results for all the problems. |
| doi_str_mv | 10.1016/j.cor.2015.05.003 |
| format | Article |
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•We formulate the representation problem in two dimensions for three different measures: uniformity, coverage, and є-indicator.•We present algorithms that solve the representation problems for the three measures in polynomial time.•We consider multiobjective variants of representation problems, and present polynomial time algorithms to solve them.•We present and discuss experimental results for all the problems.</description><identifier>ISSN: 0305-0548</identifier><identifier>EISSN: 1873-765X</identifier><identifier>EISSN: 0305-0548</identifier><identifier>DOI: 10.1016/j.cor.2015.05.003</identifier><identifier>CODEN: CMORAP</identifier><language>eng</language><publisher>New York: Elsevier Ltd</publisher><subject>Algorithms ; Computer Science ; Dynamic programming ; Facilities planning ; Location analysis ; Mathematical problems ; Multiobjective discrete optimization ; Operations Research ; Optimization ; Optimization algorithms ; Polynomials ; Representation ; Representations ; Site selection ; Studies ; Threshold algorithm ; Thresholds ; Variability</subject><ispartof>Computers & operations research, 2015-11, Vol.63, p.172-186</ispartof><rights>2015 Elsevier Ltd</rights><rights>Copyright Pergamon Press Inc. Nov 2015</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c466t-3df87e699bc537a48df101b491088e32375355a68bfa000330316010a6f6446d3</citedby><cites>FETCH-LOGICAL-c466t-3df87e699bc537a48df101b491088e32375355a68bfa000330316010a6f6446d3</cites><orcidid>0000-0003-2224-2185 ; 0000-0001-5162-2457 ; 0000-0001-7525-8901</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0305054815001185$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>230,314,776,780,881,3537,27901,27902,65306</link.rule.ids><backlink>$$Uhttps://hal.science/hal-04445555$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Vaz, Daniel</creatorcontrib><creatorcontrib>Paquete, Luís</creatorcontrib><creatorcontrib>Fonseca, Carlos M.</creatorcontrib><creatorcontrib>Klamroth, Kathrin</creatorcontrib><creatorcontrib>Stiglmayr, Michael</creatorcontrib><title>Representation of the non-dominated set in biobjective discrete optimization</title><title>Computers & operations research</title><description>This paper introduces several algorithms for finding a representative subset of the non-dominated point set of a biobjective discrete optimization problem with respect to uniformity, coverage and the ϵ-indicator. We consider the representation problem itself as multiobjective, trying to find a good compromise between these quality measures. These representation problems are formulated as particular facility location problems with a special location structure, which allows for polynomial-time algorithms in the biobjective case based on the principles of dynamic programming and threshold approaches. In addition, we show that several multiobjective variants of these representation problems are also solvable in polynomial time. Computational results obtained by these approaches on a wide range of randomly generated point sets are presented and discussed.
•We formulate the representation problem in two dimensions for three different measures: uniformity, coverage, and є-indicator.•We present algorithms that solve the representation problems for the three measures in polynomial time.•We consider multiobjective variants of representation problems, and present polynomial time algorithms to solve them.•We present and discuss experimental results for all the problems.</description><subject>Algorithms</subject><subject>Computer Science</subject><subject>Dynamic programming</subject><subject>Facilities planning</subject><subject>Location analysis</subject><subject>Mathematical problems</subject><subject>Multiobjective discrete optimization</subject><subject>Operations Research</subject><subject>Optimization</subject><subject>Optimization algorithms</subject><subject>Polynomials</subject><subject>Representation</subject><subject>Representations</subject><subject>Site selection</subject><subject>Studies</subject><subject>Threshold algorithm</subject><subject>Thresholds</subject><subject>Variability</subject><issn>0305-0548</issn><issn>1873-765X</issn><issn>0305-0548</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNp9kU9LAzEQxYMoWKsfwNuCFz1snWz-7C6eiqgVCoIoeAvZ3VmapU1qkhb005ta8eDBYSAw_F54b4aQcwoTClReD5PW-UkBVEwgNbADMqJVyfJSirdDMgIGIgfBq2NyEsIAqcqCjsj8GdceA9qoo3E2c30WF5hZZ_POrYzVEbssYMyMzRrjmgHbaLaYdSa0HiNmbh3Nynx-q0_JUa-XAc9-3jF5vb97uZ3l86eHx9vpPG-5lDFnXV-VKOu6aQUrNa-6PmVoeE2hqpAVrBRMCC2rptfJJ2PAqAQKWvaSc9mxMbna_7vQS7X2ZqX9h3LaqNl0rnYz4JyLVFua2Ms9u_bufYMhqlWyjsultug2QdFSFlBXRb1DL_6gg9t4m5IoKmtWgKBFnSi6p1rvQvDY_zqgoHa3UINKt1C7WyhInQKMyc1eg2krW4NehdagbbEzPi1Udc78o_4CMUiPNw</recordid><startdate>20151101</startdate><enddate>20151101</enddate><creator>Vaz, Daniel</creator><creator>Paquete, Luís</creator><creator>Fonseca, Carlos M.</creator><creator>Klamroth, Kathrin</creator><creator>Stiglmayr, Michael</creator><general>Elsevier Ltd</general><general>Pergamon Press Inc</general><general>Elsevier</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>1XC</scope><scope>VOOES</scope><orcidid>https://orcid.org/0000-0003-2224-2185</orcidid><orcidid>https://orcid.org/0000-0001-5162-2457</orcidid><orcidid>https://orcid.org/0000-0001-7525-8901</orcidid></search><sort><creationdate>20151101</creationdate><title>Representation of the non-dominated set in biobjective discrete optimization</title><author>Vaz, Daniel ; Paquete, Luís ; Fonseca, Carlos M. ; Klamroth, Kathrin ; Stiglmayr, Michael</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c466t-3df87e699bc537a48df101b491088e32375355a68bfa000330316010a6f6446d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Algorithms</topic><topic>Computer Science</topic><topic>Dynamic programming</topic><topic>Facilities planning</topic><topic>Location analysis</topic><topic>Mathematical problems</topic><topic>Multiobjective discrete optimization</topic><topic>Operations Research</topic><topic>Optimization</topic><topic>Optimization algorithms</topic><topic>Polynomials</topic><topic>Representation</topic><topic>Representations</topic><topic>Site selection</topic><topic>Studies</topic><topic>Threshold algorithm</topic><topic>Thresholds</topic><topic>Variability</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Vaz, Daniel</creatorcontrib><creatorcontrib>Paquete, Luís</creatorcontrib><creatorcontrib>Fonseca, Carlos M.</creatorcontrib><creatorcontrib>Klamroth, Kathrin</creatorcontrib><creatorcontrib>Stiglmayr, Michael</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>Computers & operations research</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Vaz, Daniel</au><au>Paquete, Luís</au><au>Fonseca, Carlos M.</au><au>Klamroth, Kathrin</au><au>Stiglmayr, Michael</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Representation of the non-dominated set in biobjective discrete optimization</atitle><jtitle>Computers & operations research</jtitle><date>2015-11-01</date><risdate>2015</risdate><volume>63</volume><spage>172</spage><epage>186</epage><pages>172-186</pages><issn>0305-0548</issn><eissn>1873-765X</eissn><eissn>0305-0548</eissn><coden>CMORAP</coden><abstract>This paper introduces several algorithms for finding a representative subset of the non-dominated point set of a biobjective discrete optimization problem with respect to uniformity, coverage and the ϵ-indicator. We consider the representation problem itself as multiobjective, trying to find a good compromise between these quality measures. These representation problems are formulated as particular facility location problems with a special location structure, which allows for polynomial-time algorithms in the biobjective case based on the principles of dynamic programming and threshold approaches. In addition, we show that several multiobjective variants of these representation problems are also solvable in polynomial time. Computational results obtained by these approaches on a wide range of randomly generated point sets are presented and discussed.
•We formulate the representation problem in two dimensions for three different measures: uniformity, coverage, and є-indicator.•We present algorithms that solve the representation problems for the three measures in polynomial time.•We consider multiobjective variants of representation problems, and present polynomial time algorithms to solve them.•We present and discuss experimental results for all the problems.</abstract><cop>New York</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.cor.2015.05.003</doi><tpages>15</tpages><orcidid>https://orcid.org/0000-0003-2224-2185</orcidid><orcidid>https://orcid.org/0000-0001-5162-2457</orcidid><orcidid>https://orcid.org/0000-0001-7525-8901</orcidid><oa>free_for_read</oa></addata></record> |
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| source | Elsevier ScienceDirect Journals Collection |
| subjects | Algorithms Computer Science Dynamic programming Facilities planning Location analysis Mathematical problems Multiobjective discrete optimization Operations Research Optimization Optimization algorithms Polynomials Representation Representations Site selection Studies Threshold algorithm Thresholds Variability |
| title | Representation of the non-dominated set in biobjective discrete optimization |
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